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If we don’t die we don’t evolve.Sure we will, just not in the traditional natural-selection sense. In many ways humans have "beaten" evolution by finding medical means to allow "unfit" humans to live full lives, and often pass on their genes.
Evolution in the future could be via technical means, either through advancements in medicine, or with cybernetic implants. If humans could ever become intellectually & ethically pure enough to be trusted with genetic engineering ourselves, that's another form of self-made evolution.
> If we had many lives then each one would be less meaningful.
That's a very personal thing, and just an opinion. With changes in lifespan, attitudes change, purpose changes, and people change their outlook. Once upon a time, humans lived much shorter lives, with many/most not making it out of their 30s. Now life expectancy is in the 70s and 80s. And yet we don't look at this doubling of our lifespans and believe that all that extra time robs our lives of meaning. So why should that be the case if we could live to be 500?
> We’d at least need to put age limits on political participation.
Perhaps, but that should be a floating limit that gets adjusted upward with life expectancy. If people regularly lived to be 200, maybe 190-year-olds wouldn't be fit to serve, but a 100-year-old? Why not? And if we managed to push that to 400, those 190-year-olds would start to seem pretty relevant; it would be an injustice to deny them participation in the political system.
Regardless, our idea of society itself would need a huge overhaul even if our lifespans were doubled, let alone made effectively limitless. Political participation would likely be the least of our worries.